Problem: Factor completely. $2x^4+4x^3-30x^2=$
Solution: As a first step, let's see if there's a common factor we can factor out. Greatest common factor The greatest common factor of $2x^4$, $4x^3$, and $-30x^2$ is $2x^2$. Let's factor $2x^2$ out of $2x^4+4x^3-30x^2$ : $\begin{aligned} &\phantom{=}2x^4+4x^3-30x^2 \\\\ &=2x^2(x^2)+2x^2(2x)+2x^2(-15) \\\\ &=2x^2(x^2+2x-15) \end{aligned}$ We can keep factoring the expression by factoring $x^2+2x-15$. Factoring $x^2+2x-15$ $x^2+2x-15=(x+5)(x-3)$ Putting it all together $\begin{aligned} &\phantom{=}2x^4+4x^3-30x^2 \\\\ &=2x^2(x^2+2x-15) \\\\ &=2x^2(x+5)(x-3) \end{aligned}$ In conclusion, this is the completely factored expression: $2x^2(x+5)(x-3)$